Dividing method for three-dimensional logical puzzles

ABSTRACT

A dividing method used to easily divide any given solid into perfectly interfitting parts by using at least one guiding polyhedron to establish an axis system serving as guiding paths for associated geometrical figure contours used to slice said given solid. This axis system is coincident with all or a subset of the geometrical centers of each face of the guiding polyhedron, with midpoints of the edges of the polyhedron, and with the vertices of the polyhedron. The dividing method is based on five different techniques: a selecting technique, a sizing technique, a multi-slicing technique, a multi-pivoting technique, and a multi-guiding technique. This dividing method can create extremely challenging, aesthetic and symmetrical three-dimensional puzzles having shifting and optionally sliding features. This dividing method works with polyhedron-based solids, spherical solids and odd-shaped solids of any kind.

TECHNICAL FIELD

The present invention relates generally to a dividing method useful forsimply dividing any given solid into perfectly interfitting parts, ormaking three-dimensional logical puzzles and, in particular, to puzzleshaving either a spherical shape or a shape based on a polyhedron.

BACKGROUND OF THE INVENTION

The prior art of shifting-movement puzzles includes regular, semiregularand irregular polyhedra. There are numerous types of polyhedron-basedpuzzles known in the art. Most of the prior art polyhedron puzzles arebased on the five platonic solids and are of very moderate complexity.

Also known in the art are three-dimensional sliding puzzles.Three-dimensional puzzles combining shifting and sliding features havebeen proposed by Applicant in U.S. patent application Ser. No.11/738,673 (Paquette) entitled “Three-Dimensional Logical Puzzles”,which was filed on May 2, 2007.

Also known in the art are ball-shaped or spherical puzzles. Sphericalshifting puzzles are very scarce due to the great difficulty of properlydividing a sphere in order to obtain a symmetrical, aesthetical andchallenging puzzle.

Spherical puzzles created by dividing a sphere based on a guidingregular polyhedron, i.e. by defining outer spherical sections bydividing the sphere parallel to a guiding polyhedron to createoverlapping spherical sections on the sphere, are proposed by Applicantin U.S. patent application Ser. No. 11/738,673, supra. A sphericalpuzzle created by this technique is challenging, entertaining andaesthetically pleasing.

Odd-shaped puzzles, such as a human head for example, are proposed butare of a low difficulty level again due to the complexity of the shapedivision involved.

Therefore, complexly subdivided regular, semiregular or irregularpolyhedron-based puzzles, or spherical puzzles, or odd-shaped puzzlesenabling shifting (and optionally also sliding movement) would provide ahighly challenging, entertaining and aesthetically-pleasingthree-dimensional puzzle.

SUMMARY OF THE INVENTION

An object of the present invention is to provide an easy,straightforward dividing method useful for making symmetrical,challenging, entertaining and aesthetically pleasing polyhedron-based,or spherical-based, or odd-shape-based puzzles having elements that canbe shifted and which can optionally further include superimposed slidingfeatures.

The present disclosure explains a method of dividing any given solid inperfectly interfitting parts by using an axis system associated with aguiding polyhedron. The axes are defined as passing through all or asubset of the geometrical centers of every face, edge midpoints andvertices. Each axis serves as a path along which a planar(two-dimensional) geometrical figure can be projected into anintersecting relationship with the given solid to thereby slice thegiven solid into perfectly interfitting parts according to theparticular contours of the geometrical figure. In other words, aplurality of potentially different geometrical figures, each defining acutting plane having its own geometrical contours, is used to cuts, orslice, the solid into puzzle elements by intersecting the solid with thevarious geometrical figures whose respective orientations remain fixedrelative to their respective axes.

By properly choosing a suitable guiding polyhedron, axis system andassociated geometrical figures, an infinity of aesthetic and challengingthree-dimensional puzzles can be produced from various solids.

The exposed dividing method works with polyhedron solids, spheres andodd-shaped solids of any kind. Any polyhedron can be selected as theguiding polyhedron, but the preferred ones for symmetrical reasons areof the convex uniform kind, such as the platonic solids, the archimedeansolids and the prism and antiprism solids.

The dividing method exposed in the present disclosure can be easilyextended by using superposed polyhedra for guiding purposes, all ofwhich lies within the scope of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the present invention will now be described withreference to the appended drawings in which:

FIG. 1 is a schematic representation of the proposed dividing method;

FIG. 2 illustrates a sphere divided in rotating, mobile and gap elementsby circular geometrical figures associated with a guiding tetrahedron;

FIG. 3 is showing a geometrical figure circular radius r_(ng) selectedto eliminate the gap elements (tetrahedron face guided);

FIG. 4 is showing a sphere divided by a circular geometrical figure witha circular radius smaller than the no-gap radius r_(ng) (tetrahedronface guided);

FIG. 5 presents the outcome of a dividing radius superior to the no-gapradius r_(ng) (tetrahedron face guided) illustrating the sizingtechnique of the dividing method;

FIG. 6 shows a double slicing at radius r_(2ng) and r_(max) of thesphere from FIG. 5 representing the multi-slicing technique aspect ofthe dividing method (tetrahedron face guided);

FIG. 7 also illustrates a double-slicing of a sphere from FIG. 5 with asecond radius non-equal to the no-gap radius r_(2ng) (tetrahedron faceguided);

FIG. 8 illustrates a combination of a double-sliced circular tetrahedronface division with a circular tetrahedron vertex division presenting themulti-pivoting technique of the dividing method;

FIG. 9 illustrates a circular dodecahedron face division of a sphere;

FIG. 10 is a circular dodecahedron face division of a sphere at theno-gap radius r_(dng);

FIG. 11 illustrates the outcome of a dividing radius superior to theno-gap radius r_(dng) (dodecahedron face guided);

FIG. 12 illustrates a double-sliced circular dodecahedron face divisionof a sphere;

FIG. 13 is showing a circular icosahedron face division of a sphere;

FIG. 14 shows a combination of a single-sliced circular icosahedron facedivision with a multi-pivoting single-sliced circular icosahedron vertexdivision of a sphere;

FIG. 15 is a schematic representation of the dividing method applied toa cube using an octahedron guiding polyhedron;

FIG. 16 illustrates a single-sliced six-pointed star octahedron face tocube vertex division, with a single-sliced octahedral octahedron vertexto cube face division, and a single-sliced hexahedral octahedron edge tocube edge division of a cube for non-puzzle purposes;

FIG. 17 illustrates a single-sliced circular octahedron face to cubevertex division of a cube suited for puzzle purposes;

FIG. 18 is a combination of a single-sliced circular octahedron face tocube vertex division with a mutli-pivoting single-sliced circularoctahedron vertex to cube face division applied to a cube;

FIG. 19 illustrates an exploded view of an odd-shape puzzle divided by asingle-sliced tetrahedron face division;

FIG. 20 is an assembled view of FIG. 19 showing the extendedpossibilities of the dividing method applicable to any odd-shaped solid.

These drawings are not necessarily to scale, and therefore componentproportions should not be inferred therefrom.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

By way of introduction, the dividing method will be illustrated withsimple preferred embodiments related to a regular guiding polyhedron. Itis to be understood that any polyhedron or combination of polyhedra canbe used as the guiding polyhedron associated with said axis system, allwithin the scope of the present invention.

The dividing method presented in this disclosure consists of acombination of techniques, a selecting technique, a sizing technique, amulti-slicing technique, a multi-pivoting technique, and a mutli-guidingtechnique used to create symmetrical, aesthetic and challenging puzzles,or simply used to divide any given solid into perfectly interfittingparts. Of the five techniques presented herein only the two first areessential to the dividing method. The three remaining techniques areoptionally used to enhance the puzzle's complexity in order to achieve agreater challenge.

Reference is now made to FIG. 1. In this schematic representation of thedividing method, the given solid to be divided is represented by asphere S with an inscribed tetrahedron T. The guiding tetrahedron couldhave been shown inscribed or subscribed without any differences since itis the axis system associated with the polyhedron that is relevant tothe dividing method. For each face of the guiding polyhedron there is anassociated axis f-f also associated with a geometrical figure F. Eachaxis f-f, four in the case of a tetrahedron, can be associated with adifferent geometrical figure F, or share the same one. The axis systemis completed by having vertex axis v-v and midpoint edge axis e-eassociated respectively with geometrical figures V and E. The precedingselection of the guiding polyhedron, axis system, and associatedgeometrical figures is said to be the selecting technique of thedividing method. It is the contour of the associated geometrical figuresthat will be used through projection along their respective axes todivide, or slice, the given solid into perfectly interfitting parts.

As mentioned the first technique involved in the dividing method is theselecting technique. This technique refers mainly to the selection ofthe proper form of every geometrical figure associated with anappropriate axis system to be used for slicing the given solid. Thesecond technique involved in the dividing method is the sizingtechnique. This technique refers to the selection of the properdimension, or size, of every associated geometrical figure. Properselection of the geometrical figures and proper sizing of these figuresare essential to the dividing method and depend on the expected purposesof the divided solid. As a general rule for puzzle purposes, verysymmetrical parts are sought and as many as possible parts should beinterchangeable (shifting-wise). So mostly circular figures are used forpuzzle purposes with quite a bit of overlapping of the geometricalfigures.

Reference is now made to FIG. 2 illustrating a sphere divided by acircular geometrical figure of radius r associated with the face axisf-f of a guiding tetrahedron T. The sphere is divided into four rotatingelements 21, six mobile elements 22 and four gap elements 23.

The mobile elements 22 are grouped around each of the rotating elements21 in shifting sections whereby mobile elements of one group can beinterchanged with mobile elements of other groups. Thus, a shiftingspherical puzzle is created by dissecting a sphere with cutting circulargeometrical figures that are associated with each face axis f-f of aguiding tetrahedron T to generate overlapping outer spherical sections,each centered about a respective rotating element 21.

Necessary adjustments to convert the given solid elements into afunctioning puzzle are well described in the prior art and need nofurther explanation other than mentioning that:

(i) each rotating element is connected to the puzzle by a retainingmeans, i.e. a fastener, fastener subassembly, retainer or otherretaining mechanisms. These retaining means hold the pieces in aninterfitting relationship and enable rotational movement around theassociated axis. These retaining means could include a coil spring toreduce friction generated between adjoining surfaces and provide easilymovable elements that are not prone to jamming, catching or getting“hung up”. These interconnecting means could be replaced bysnapping-action parts, which would also fall within the scope of thepresent invention;

(ii) holding means are provided for holding the remaining elements in aninterfitting relationship with each respective rotating element, oradjacent remaining elements. Usually, the angles formed in the dividedparts are such that remaining elements cannot slide out of their fittedposition, thus preventing disassembly of the puzzle. Otherinterfittings, mechanisms or locking means are possible that enableelements to be interchanged from one group or subgroup to another groupor subgroup by “shifting” (i.e. twisting or rotating) one group orsubgroup relative to the other groups or subgroups. For example, lockingmeans could include a tongue and groove mechanism. It is understood thatthis groove could be male (protrusion) or female (cavity), and of manyshapes like dovetail-shaped, L-shaped or T-shaped or of any shape thatprovides a retaining means allowing rotation about an axis, all withinthe scope of the present invention;

(iii) the obtained puzzle can be designed with or without a centerelement or core located inside of the given solid puzzle, which can beeither (a) an inner sphere, or (b) an internal concentric polyhedron, or(c) an axial rod (pivot) system. Depending on the guiding polyhedronused and the selected dividing geometrical figures, the center elementmay or may not have exposed faces. A coreless puzzle can be constructedby providing the rotating elements, mobile elements, gap elements, andthe remaining elements, if applicable, with appropriate protrusions andgrooves. These protrusions and grooves cooperate as interfitting maleand female connections to slideably and rotatably interlock the variouselements to thus hold the elements together to form a complete solidpuzzle. Also, the center element could be constructed by theinterfitting or snapping action of two half center core elements. Whenassembled together these two half center core elements form a hollowcenter core element shaped as a polyhedron or a sphere. With this hollowcenter core element, the rotating elements are rotationally connected tothe core element by a screw inserted from inside the puzzle and thus nocapping of elements is required in order to obtain an even and smoothouter surface over the given solid outer shell of the puzzle. All of thepreviously mentioned possibilities or modifications lie within the scopeof the present invention.

The foregoing adjustments (or other similar adjustments well within thecapabilities of a person of ordinary skill in the art) are needed toconvert the given solid elements in the puzzles presented in theremaining figures of this disclosure so as to obtain functioning(shiftable) puzzles. These modifications and adjustemnts are well withinthe reach of a person familiar with the art of three-dimensional puzzlesand therefore require no further elaboration.

FIG. 3 to FIG. 5 illustrate the huge influence that the sizing techniquehas on the resulting puzzle parts. That influence is translated intodifferent types, forms and numbers of elements.

Reference is now made to FIG. 3 which shows a spherical solid divided bycircular geometrical figures of radius r_(ng) associated with the faceaxis of a guiding tetrahedron. It is the exact same selecting techniqueof the dividing method used in FIG. 2 except that the sizing of thecircular geometrical figures is selected to eliminate the gap elements23 of FIG. 2. This is achieved when the slicing contours meet at pointP. Thus the obtained puzzle only has two types of elements, rotatingelements 31 and mobile elements 32.

Reference is now made to FIG. 4 showing the result of the exact sameselecting technique of the dividing method used in FIG. 2 and FIG. 3with a circular radius r_(u) of the geometrical figures sized smallerthan the no-gap radius r_(ng). This division of the given solid is saidto be “tetrahedron face guided” exactly as with the previous puzzle.This puzzle is constituted of three types of elements, pivoting elements41, mobile elements 42, and gap elements 43.

Reference is now made to FIG. 5 illustrating a tetrahedron face guideddivision of a sphere with a sizing of the circular geometrical figureradius r_(max) superior to the no-gap radius r_(ng). This puzzle is alsoconstituted of three types of elements, pivoting elements 51, mobileelements 52, and gap elements 53 of different size and shape compared tothe puzzle depicted in FIG. 4.

FIG. 6 and FIG. 7 illustrate the multi-slicing technique used toincrease the number of parts that are interchangeable on a given solidpuzzle. This multi-slicing technique is simple, straightforward and veryefficient in creating challenging symmetrical puzzles.

Reference is now made to FIG. 6 where the multi-slicing technique ispresented in the form of a double slicing at radius r_(max) and r_(2ng)(contours meeting at point P) of the sphere from FIG. 5. The sphericalpuzzle is now constituted of five different types of elements, rotatingelements 61, mobile elements 62, secondary mobile elements 63, secondarygap elements 64, and inter-gap elements 65. Since the multi-slicingtechnique of a given solid puzzle using the same proposed selecting andsizing techniques will easily result in a different quantity of elementsand different types of elements, it allows one to vary the total numberof puzzle puzzle elements to achieve either simpler or more complexpuzzles. It is to be understood that these simpler or more complexpuzzles are within the scope of the invention presented in thisdisclosure. Also to be understood is that various combinations, changesor modifications are possible giving almost an infinity of possibilitiesif the dividing method is used with other regular, semiregular,irregular, spherical or odd-shaped given solid.

Reference is now made to FIG. 7 illustrating a tetrahedron face guideddouble-slicing of the sphere from FIG. 5 with a first radius r₁ and asecond radius r₂ different from the no-gap radius r_(2ng). The outcomeof this division is now six different types of elements, rotatingelements 71, mobile elements 72, secondary mobile elements 73, secondarygap elements 74, inter-gap elements 75, and gap elements 76.

FIG. 8 presents another technique being part of the dividing method, themulti-pivoting technique. This technique is used to incorporate pivotingfeatures around previously non-pivoting elements. The multi-pivotingtechnique is also very simple, straightforward and also very efficientfor increasing the number of parts interchangeable on a given solidpuzzle, thus creating ultimately challenging symmetrical puzzles.

Reference is now made to FIG. 8 illustrating the puzzle of FIG. 7submitted to the multi-pivoting technique by introducing a said“tetrahedron vertex division” through circular geometrical figures ofradius r₃. This tetrahedron vertex division is carried along axescoincident with the guiding polyhedron vertices. It can be appreciatedthat the complexity of the puzzle rapidly increases. The puzzle beingnow constituted of ten elements, rotating elements 81, mobile elements82, secondary mobile elements 83, secondary gap elements 84, inter-gapelements 85, gap elements 86, secondary pivoting elements 87, firstinter-mobile elements 88A, second inter-mobile elements 88B, andtertiary mobile elements 89.

The last technique of the dividing method, the “multi-guidingtechnique”, relates to the use of multiple guiding polyhedra used todivide one given solid. This technique corresponds to the superpositionof different divisions from different puzzles into only one puzzle. Theresults of such superposition becomes rapidly complex and for the sakeof simplicity only puzzles based on single guiding polyhedra arepresented in this disclosure. However, it will be obvious to a personfamiliar with the art of three-dimensional puzzles, that this techniquealone is an extremely powerful tool to create astonishingly complex andintriguing puzzles aimed at the expert enthusiast. But as mentioned inthe prior art, with proper indicia pattern selection, the puzzledifficulty level can be modulated to obtain a reasonably solvablepuzzle. FIG. 9 to FIG. 18 will now be devoted to illustrate the power ofchanging the guiding polyhedron used to divide a simple solid. This willenable a puzzle developer to appreciate the powerful dividing methoddisclosed herein. It is to be mentioned that only some of the fiveplatonic solids are used as the guiding polyhedron in the presentdisclosure, but that any polyhedron showing some kind of symmetry can beused for puzzle purposes. This requirement is not necessary if only adivision of a given solid into perfectly interfitting parts is sought.Accordingly, the best suited polyhedra to be used in the dividing methodfor puzzle purposes are of the convex uniform kind, such as the fiveplatonic solids, the thirteen archimedean solids, and mostly all of theprism and antiprism solids.

Reference is now made to FIG. 9 illustrating a circular dodecahedronface division of a sphere. The associated geometrical figures arecircular with a contour radius r_(d). The result of this division istwelve pivoting elements 91, thirty mobile elements 92, and twenty gapelements 93. This exact puzzle is presented in the prior art with adifferent dividing method. The dividing method of the present disclosureis more general.

Reference is now made to FIG. 10 showing a circular dodecahedron facedivision of a sphere at the no-gap radius r_(dng). With such a radiusthe contours projected on the sphere surface meet at point P, and thusno gap elements are produced leaving only pivoting elements 101 andmobile elements 102 covering the entire outer surface of the dividedsphere. One can contemplate that the effect of the sizing technique isvery similar either with a tetrahedron guided division or a dodecahedronguided division.

Reference is now made to FIG. 11 showing quite a large differencebetween elements of the present figure compared to elements of FIG. 9.This large difference is obtained simply by enlarging the associatedgeometrical figure contour radius r_(d). There are also three types ofelements obtained by this division, pivoting elements 111, mobileelements 112, and gap elements 113. Puzzlewise, such a configuration issuperior since a larger portion of the sphere's surface moves whileplaying the puzzle. So the fixed portion and the moving portion of apuzzle surface can be adjusted by the puzzle designer at will. Thisconstitutes a big advantage when adapting the puzzle to differentpurposes, such as creating promotional vehicles, designing simple puzzlefor kids or designing complex puzzles for the expert puzzle enthusiast.

Reference is now made to FIG. 12 in which a double-sliced circulardodecahedron face division applied to a sphere such as the one in FIG.11 is shown. This double-slicing is carried with the same geometricalfigure along the same guiding axis, except with two different radiir_(d1) and r_(d2). It can be appreciated that a very interesting,symmetrical puzzle is obtained. This puzzle being constituted of sixdifferent types of elements, pivoting elements 121, mobile elements 122,gap elements 123, secondary mobile elements 124, secondary gap elements125, and inter-gap elements 126. Here also the dedocahedronmulti-slicing division is very similar to the tetrahedron multi-slicingdivision.

Reference is now made to FIG. 13 showing a circular icosahedron facedivision of a sphere at radius r_(i). Since the guiding polyhedron is anicosahedron there will be twenty pivoting elements 131, with theremaining of the puzzle's outer surface covered by mobile elements 132and gap elements 133. Due to the great number of pivoting elementsinvolved one can anticipate that the icosahedron family puzzles would bevery challenging.

Reference is now made to FIG. 14 illustrating an application of themulti-pivoting technique applied to the icosahedron-based puzzle of FIG.13, sliced at radius r_(i2). The number of different elements is nowfive, namely pivoting elements 141, mobile elements 142, gap elements143, secondary mobile elements 144, and secondary pivoting elements 145.Great similarities exist with the previous puzzles. It is possible toanticipate a large magnitude of permutations resulting from theapplication of a mutli-slicing technique to such an icosahedron-basedpuzzle. Also, by introducing a multi-guiding technique to this family ofpuzzles, a countless number of puzzles could be obtained, and thesewould be almost impossible to solve unless appropriate visual indiciapatterns were used to modulate (simplify) the difficulty level of thesepuzzles.

Reference is now made to FIG. 15 showing the proposed dividing methodapplied to a cubic solid. In this schematic representation of thedividing method, the given solid to be divided is represented by a cubeC with an inscribed octahedron 0. For each face of the guidingpolyhedron there is an associated axis f-f passing through a cubevertex, since the guiding octahedron is positioned such that itsvertices are coincident with the geometrical centers of each cube face(point po). Not shown are associated geometrical figures F. The axissystem is completed by having vertex axis v-v passing through thegeometrical centers of each cube face, and midpoint edge axis e-epassing through cube edge midpoints. Also not shown are the associatedgeometrical figures V and E. The contours of the associated geometricalfigures F, V, E are then used through projection along their respectiveaxes to divide, or slice, the cubic solid into perfectly interfittingparts.

Reference is now made to FIG. 16 in which the associated geometricalfigures F are six-pointed stars, the figures V are octagonals, andfigures E are hexagonals used for dividing the cube-shaped solid. Thepreceding division is described as a single-sliced six-pointed staroctahedron face to cube vertex division, with a single-sliced octagonaloctahedron vertex to cube face division, with a single-sliced hexagonaloctahedron edge to cube edge division of a cube. The resulting dividedcube is not realistically intended to be implemented as a puzzle, butthis however illustrates the extreme possibilities of the dividingmethod.

Reference is now made to FIG. 17 illustrating a single-sliced circularoctahedron face to cube vertex division of a cube suited for puzzlepurposes. This division being carried at radius r_(c). The resultingcube is of a completely novel aspect. The complete cube can be assembledfrom only four different types of elements, pivoting elements 171,mobile elements 172, secondary gap elements 173, and gap elements 174.Again many similarities can be observed with the preceding puzzles.

Reference is now made to FIG. 18 where a combination of a single-slicedcircular octahedron face to cube vertex division with a mutli-pivotingsingle-sliced circular octahedron vertex to cube face division is shownand applied to a cube. These two divisions are carried at radius r_(c1)and r_(c2). A very interesting cubic puzzle is than easily obtained bythe application of the present dividing method. The resulting puzzle isconstituted of six different types of elements, namely pivoting elements181, mobile elements 182, secondary gap elements 183, gap elements 184,secondary pivoting elements 185, and secondary mobile elements 186. Thispuzzle can be easily complicated by applying other techniques availablein the dividing method giving almost an infinity of possibilities.

Reference is now made to FIG. 19 illustrating an exploded view of anodd-shaped solid divided by a single-sliced tetrahedron face division.In this figure, only the pivoting elements are identified. It is to benoted that each one has a different form. There are four pivotingelements, since a single-sliced tetrahedron face division is used,element 191, element 192, element 193, and element 194. They are allobtained from a division with circular geometrical figure of radiusr_(h).

Reference is now made to FIG. 20 showing an assembled view of theodd-shaped solid of FIG. 19. These two figures present the extendedpossibilities of the dividing method applicable to any odd-shaped solid.

It is to be understood that the same techniques for arranging thedisplay of colours, emblems, logos or other visual indicia on the outersurfaces of the puzzles to modulate the difficulty level of the puzzlespresented in the prior art are also applicable to any of the puzzlesobtained through the application of the dividing method disclosedherein. Complex descriptions of evoluted patterns are not included inthe present disclosure for the sake of simplicity, but are well withinthe scope of the technology introduced here and can be easily derivedfrom the principles already disclosed in the prior art and applied tothe puzzles resulting from the present dividing method. Different visualindicia patterns (e.g. colours, logos, emblems, symbols, etc.) can beused to modulate the difficulty level of the puzzles. In other words,different versions of a given puzzle can be provided for novice,intermediate or expert players, or even for kids.

It should be noted that advertising, corporate logos or team logos couldalso be placed onto the surfaces of the puzzles obtained by theapplication of the present dividing method to create promotionalvehicles or souvenirs.

Also worth mentioning is that it is possible to add sliding movements tothe pre-existing shifting movement to further complicate the puzzles.Slidable elements can be added to underlying shiftable elements asdescribed Applicant's U.S. patent application Ser. No. 11/738,673.Generally, this is done by superimposing permutable sliding elements atthe outer face of a given puzzle that slide in grooves in the underlyingfaces of said given puzzle to provide both shifting and slidingmovements. Each superimposed sliding element slides in a curved track(the adjoining grooves) over the outer faces of non-sliding given puzzleelements along a circular slideway groove formed by adjacent grooves.Thus, adding sliding elements to a given shifting puzzle greatlyincreases the complexity of said given puzzle. Such given puzzle is nowsaid to combine both shifting and sliding features.

All the aforesaid sliding modifications are analogous to themodifications introduced in Applicant's U.S. patent application Ser. No.11/738,673, and therefore need not be repeated herein.

Other polyhedra of any kind could also be used as the guiding polyhedronfor bisecting any given solid with the present dividing method, allwithout departing from the scope of the present invention. Likewise, thedividing method could also be applied to any polyhedron to achieve andcreate other interesting and challenging puzzles. Accordingly, thedrawings and description are to be regarded as being illustrative, notas restrictive.

It will be noted that exact dimensions are not provided in the presentdescription since these puzzles can be constructed in a variety ofsizes.

While the puzzle elements and parts are preferably manufactured fromplastic, these puzzles can also be made of wood, metal, or a combinationof the aforementioned materials. These elements and parts may be solidor hollow. The motion of the puzzle mechanism can be enhanced byemploying springs, bearings, semi-spherical surface knobs, grooves,indentations and recesses, as is well known in the art and are alreadywell described in the prior art of shifting and sliding puzzles.Likewise, “stabilizing” parts can also be inserted in the mechanism tobias the moving elements to the “rest positions”, as is also well knownin the art.

It is understood that the above description of the preferred embodimentsis not intended to limit the scope of the present invention, which isdefined solely by the appended claims.

1. A method of dividing any given solid into perfectly interfittingparts covering an entire outer surface of a shiftable three-dimensionalpuzzle, the method comprising steps of: selecting at least one guidingpolyhedron; defining an axis system based on the at least one guidingpolyhedron, wherein axes of the axis system passthrough all or a subsetof geometrical centers of the faces, edges and vertices of the guidingpolyhedron; associating, with each axis, a planar geometrical figurecontour which can be projected along each respective axis into anintersection with the given solid to be divided; and dividing the givensolid using the geometrical figure contour into perfectly interfittingparts covering the entire outer surface of the puzzle.
 2. The dividingmethod as claimed in claim 1 wherein the step of associating thegeometrical figure contour with each axis comprises steps of selecting aproper form for each geometrical figure contour associated with the axesof the axis system and sizing each geometrical figure contour fordividing the given solid.
 3. The dividing method as claimed in claim 2further comprising a step of applying a multi-slicing technique whereinsaid given solid is sliced more than once along one or more of the axesof the axis system with geometrical figure contours of a different size.4. The dividing method as claimed in claim 2 further comprising a stepof applying a multi-pivoting technique wherein a circular geometricalfigure contour is added to one or more axes of the axis system to dividesaid given solid into pivoting groups of one or more elements.
 5. Thedividing method as claimed in claim 2 further comprising a step ofapplying a multi-guiding technique wherein one or more guiding polyhedraare superimposed as guides for multiple axis systems, with axes passingthrough all or a subset of geometrical centers of faces, edges andvertices of the guiding polyhedral whereby each axis of every additionalaxis system is associated with a geometrical figure contour which can beprojected into an intersecting relationship with the solid in order toslice the given solid into perfectly interfitting parts covering theentire outer surface of the solid.
 6. The dividing method as claimed inclaim 1 comprising at least one of the steps of: selecting a proper formfor each geometrical figure contour associated with axes of the axissystem; sizing each geometrical figure contour to be used for slicingthe given solid; applying a a multi-slicing technique wherein the givensolid is sliced more than once along at least one axis of the axissystem with a geometrical figure contour of a different size; applying amulti-pivoting technique wherein a circular geometrical figure contouris added to at least one axis of the axis system to divide said givensolid into pivoting group of one or more elements; and applying amulti-guiding technique wherein one or more guiding polyhedra aresuperimposed as guides for axis systems, with axes passing through allor a subset of geometrical centers of faces, edges and vertices of theguiding polyhedra, whereby each axis of each additional axis system isassociated with a geometrical figure contour along which the geometricalfigure contour can be projected into an intersecting relationship withthe solid in order to slice the given solid into perfectly interfittingparts covering the entire outer surface of the solid.
 7. The dividingmethod as claimed in claim 6 wherein the guiding polyhedra are convexuniform polyhedra selected from the five platonic solids, the thirteenarchimedean solids, the prism solids, and the antiprism solids.
 8. Thedividing method as claimed in claim 7 wherein most of the associatedgeometrical figure contours are circular in order to create a mostlysymmetrical three-dimensional puzzle when said given solid is divided,wherein some of the interfitting parts act as pivoting elements whileenabling substantially all of the other parts of the puzzle to beshifted.
 9. The dividing method as claimed in claim 8 wherein said givensolid is a polyhedron.
 10. The dividing method as claimed in claim 9comprising a further step of superimposing sliding elements onto one ormore outer surfaces of said puzzle.
 11. The dividing method as claimedin claim 8 wherein said given solid is a sphere.
 12. The dividing methodas claimed in claim 11 comprising a further step of superimposingsliding elements onto one or more outer surfaces of said puzzle.
 13. Thedividing method as claimed in claim 8 wherein said given solid is anodd-shaped solid.
 14. The dividing method as claimed in claim 13comprising a further step of superimposing sliding elements onto one ormore outer surfaces of said puzzle.